Datasets:
ai-metrology-lab
/
MathBode-LinearSystem

Dataset card Data Studio Files
xet
Community
1
family
stringclasses
1 value
question_id
int64
0
2
signal_type
stringclasses
2 values
amplitude_scale
float64
0.5
2.5
frequency_cycles
float64
1
16
phase_deg
float64
0
240
⌀
time_step
int64
0
255
p_value
float64
3.5
4.5
prompt
stringlengths
59
76
ground_truth
float64
0.52
2.33
symbolic_baseline_answer
float64
0.52
2.33
linear_system
1
sinusoid
1
4
0
32
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
4
0
33
4.076537
Solve this system for x: 4.076536686473018x + 2y = 8 1x + 3y = 9 FINAL:
0.586533
0.586533
linear_system
1
sinusoid
1
4
0
34
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
4
0
35
4.184776
Solve this system for x: 4.184775906502257x + 2y = 8 1x + 3y = 9 FINAL:
0.568487
0.568487
linear_system
1
sinusoid
1
4
0
36
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
4
0
37
4.184776
Solve this system for x: 4.184775906502257x + 2y = 8 1x + 3y = 9 FINAL:
0.568487
0.568487
linear_system
1
sinusoid
1
4
0
38
4.141421
Solve this system for x: 4.14142135623731x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
4
0
39
4.076537
Solve this system for x: 4.076536686473018x + 2y = 8 1x + 3y = 9 FINAL:
0.586533
0.586533
linear_system
1
sinusoid
1
4
0
40
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
4
0
41
3.923463
Solve this system for x: 3.9234633135269825x + 2y = 8 1x + 3y = 9 FINAL:
0.6141
0.6141
linear_system
1
sinusoid
1
4
0
42
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
4
0
43
3.815224
Solve this system for x: 3.8152240934977426x + 2y = 8 1x + 3y = 9 FINAL:
0.635212
0.635212
linear_system
1
sinusoid
1
4
0
44
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
4
0
45
3.815224
Solve this system for x: 3.8152240934977426x + 2y = 8 1x + 3y = 9 FINAL:
0.635212
0.635212
linear_system
1
sinusoid
1
4
0
46
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
4
0
47
3.923463
Solve this system for x: 3.923463313526982x + 2y = 8 1x + 3y = 9 FINAL:
0.6141
0.6141
linear_system
1
sinusoid
1
4
0
48
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
4
0
49
4.076537
Solve this system for x: 4.076536686473018x + 2y = 8 1x + 3y = 9 FINAL:
0.586533
0.586533
linear_system
1
sinusoid
1
4
0
50
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
4
0
51
4.184776
Solve this system for x: 4.184775906502257x + 2y = 8 1x + 3y = 9 FINAL:
0.568487
0.568487
linear_system
1
sinusoid
1
4
0
52
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
4
0
53
4.184776
Solve this system for x: 4.184775906502257x + 2y = 8 1x + 3y = 9 FINAL:
0.568487
0.568487
linear_system
1
sinusoid
1
4
0
54
4.141421
Solve this system for x: 4.14142135623731x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
4
0
55
4.076537
Solve this system for x: 4.076536686473018x + 2y = 8 1x + 3y = 9 FINAL:
0.586533
0.586533
linear_system
1
sinusoid
1
4
0
56
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
4
0
57
3.923463
Solve this system for x: 3.9234633135269825x + 2y = 8 1x + 3y = 9 FINAL:
0.6141
0.6141
linear_system
1
sinusoid
1
4
0
58
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
4
0
59
3.815224
Solve this system for x: 3.8152240934977426x + 2y = 8 1x + 3y = 9 FINAL:
0.635212
0.635212
linear_system
1
sinusoid
1
4
0
60
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
4
0
61
3.815224
Solve this system for x: 3.8152240934977426x + 2y = 8 1x + 3y = 9 FINAL:
0.635212
0.635212
linear_system
1
sinusoid
1
4
0
62
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
4
0
63
3.923463
Solve this system for x: 3.923463313526982x + 2y = 8 1x + 3y = 9 FINAL:
0.6141
0.6141
linear_system
1
sinusoid
1
8
0
0
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
1
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
2
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
8
0
3
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
4
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
5
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
6
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
8
0
7
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
8
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
9
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
10
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
8
0
11
4.141421
Solve this system for x: 4.14142135623731x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
12
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
13
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
14
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
8
0
15
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
16
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
17
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
18
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
8
0
19
4.141421
Solve this system for x: 4.14142135623731x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
20
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
21
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
22
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
8
0
23
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
24
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
25
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
26
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
8
0
27
4.141421
Solve this system for x: 4.14142135623731x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
28
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
29
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
30
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
8
0
31
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
32
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
33
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
34
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
8
0
35
4.141421
Solve this system for x: 4.14142135623731x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
36
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
37
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
38
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
8
0
39
3.858579
Solve this system for x: 3.8585786437626903x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
40
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
41
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
42
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
8
0
43
4.141421
Solve this system for x: 4.14142135623731x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
44
4
Solve this system for x: 4.000000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
45
3.858579
Solve this system for x: 3.8585786437626908x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
46
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
8
0
47
3.858579
Solve this system for x: 3.8585786437626908x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
48
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
49
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
50
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
8
0
51
4.141421
Solve this system for x: 4.14142135623731x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
52
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
53
3.858579
Solve this system for x: 3.8585786437626908x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
54
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
8
0
55
3.858579
Solve this system for x: 3.8585786437626908x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
56
4
Solve this system for x: 3.9999999999999996x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
57
4.141421
Solve this system for x: 4.141421356237309x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
58
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
8
0
59
4.141421
Solve this system for x: 4.14142135623731x + 2y = 8 1x + 3y = 9 FINAL:
0.57558
0.57558
linear_system
1
sinusoid
1
8
0
60
4
Solve this system for x: 4.000000000000001x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
8
0
61
3.858579
Solve this system for x: 3.8585786437626908x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
8
0
62
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298
linear_system
1
sinusoid
1
8
0
63
3.858579
Solve this system for x: 3.8585786437626908x + 2y = 8 1x + 3y = 9 FINAL:
0.626584
0.626584
linear_system
1
sinusoid
1
16
0
0
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
16
0
1
4.2
Solve this system for x: 4.2x + 2y = 8 1x + 3y = 9 FINAL:
0.566038
0.566038
linear_system
1
sinusoid
1
16
0
2
4
Solve this system for x: 4.0x + 2y = 8 1x + 3y = 9 FINAL:
0.6
0.6
linear_system
1
sinusoid
1
16
0
3
3.8
Solve this system for x: 3.8x + 2y = 8 1x + 3y = 9 FINAL:
0.638298
0.638298